A General Three-Parameter Logistic Model With Time Effect

Within the framework of item response theory, a new and flexible general three-parameter logistic model with response time (G3PLT) is proposed. The advantage of this model is that it can combine time effect, ability, and item difficulty to influence the correct-response probability. In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden's model. In addition, the Metropolis–Hastings within Gibbs sampling algorithm is employed to estimate the model parameters. Based on Markov chain Monte Carlo output, two Bayesian model assessment methods are used to assess the goodness of fit between models. Finally, two simulation studies and a real data analysis are performed to further illustrate the advantages of the new model over the traditional three-parameter logistic model.